We have performed dispersion-corrected density-functional transition state calculations on atomic Au and atomic Pd anion catalysis of water to peroxide. From the energy barrier calculations and the thermodynamics of the reactions, we conclude that the atomic Au anion is an excellent catalyst; however, by comparison the atomic Pd anion has a higher catalytic effect on the formation of peroxide. The formation of [Au(H2O)2] and [Pd(H2O)2] anion molecular complexes in the transition state is identified as the fundamental mechanism for breaking the hydrogen bonding strength during the water catalysis, namely, the mechanism of nanocatalysis through negative ion resonances. Our theoretical results provide crucial insight into the mechanism of atomic Au and atomic Pd anion catalysis in good agreement with recent experimental observations.